Abstract
Stochastic nonlinear dependencies have been reported extensively between different uncertain parameters or in their time or spatial variance. However, the description of dependency is commonly not provided except a linear correlation. The structural reliability incorporating nonlinear dependencies thus needs to be addressed based on the linear correlations. This paper first demonstrates the capture of nonlinear dependency by fitting various bivariate non-Gaussian copulas to limited data samples of structural material properties. The vine copula model is used to enable a flexible modeling of multiple nonlinear dependencies by mapping the linear correlations into the non-Gaussian copula parameters. A sequential search strategy is applied to achieve the estimate of numerous copula parameters, and a simplified algorithm is further designed for reliability involving stationary stochastic processes. The subset simulation is then adopted to efficiently generate random variables from the corresponding distribution for high reliability evaluation. Two examples including a frame structure with different stochastic material properties and a cantilever beam with spatially variable stochastic modulus are investigated to discuss the possible effects of nonlinear dependency on structural reliability. Since the dependency can be determined qualitatively from limited data, the proposed method provides a feasible way for reliability evaluation with prescriptions on correlated stochastic parameters.
Highlights
[1]. e failure probability of a structural system is defined as the integral of the joint probability density function (PDF) fX(X) of the random vector X over the failure domain defined by the performance function G(X) ≤ 0: pf
Correlations are reported between wind speed and wind direction or between Young’s modulus and Poisson’s ratio [2, 3]. e time-dependent or spatially variable stochastic parameter that is often characterized by a stochastic process can be viewed as correlated random variables
Concluding Remarks e investigation to the uncertainties of low carbon steel properties demonstrates the possible nonlinear dependencies in practice. The incorporation of this nonlinearity into reliability analysis under the ubiquitous linear correlations is not addressed. is paper extends the subset simulation to structural reliability involving nonlinear dependencies and investigates its effect. e vine copula model is adopted to allow for modeling of multiple nonlinear dependencies, while the model parameters are estimated from linear correlations by a sequential search strategy. e algorithm for model parameter searching is optimized so that high-dimensional reliability problems involving time or spatial variance can be handled efficiently
Summary
Compared to the rank correlations, the retrieval of copula parameters from the linear correlations is more complicated because the estimate depends on both the copula function and the marginal distributions [18]. Once the joint probability distribution is represented in terms of vine copulas, the isoprobabilistic transformation for nonlinear dependent random variable can be integrated into the reliability approach. E main objectives are to demonstrate the possible nonlinear dependencies in practice and assess its impact on high structural reliability
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